Question

The figure shows an ancient coin. The coin is in the shape of a circle of
radius 3 cm with a square of sides x cm removed from its centre.
The area of each face of the coin is 71 sq cm.
i. Form an equation in x and solve it for x.
ii. Find the perimeter of the square. (Take n = 3.14)​

Answer 1

x = 4.6 cm and perimeter is 18.4 cm.

Step-by-step explanation:

See the attached figure. There is a circular coin of radius 3 cm and a whole of square shape at the center of the circle with sides x cm. And the area of each face of the coin is 7.1 sq cm.

i. Therefore, from the above conditions, an equation of x can be made and it is

πr² - x² = 7.1 ......... (1)

⇒ $\frac{22}{7}\times (3)^{2} - x^{2} = 7.1$

⇒ 28.28 - x² = 7.1

⇒ x² = 21.18

⇒ x = 4.6 cm. (Answer)

ii. The perimeter of the square is = 4x = 4 × 4.6 = 18.4 cm (Answer)